The phonon density of states and adiabatic sound velocities were measured on fcc-stabilized 242Pu0.95Al0.05. The phonon frequencies and sound velocities decrease considerably (soften) with increasing temperature despite negligible thermal expansion. The frequency softening of the transverse branch along the [111] direction is anomalously large ( approximately 30%) and is very sensitive to alloy composition. The large magnitude of the phonon softening is not observed in any other fcc metals and may arise from an unusual temperature dependence of the electronic structure in this narrow 5f-band metal.